Quantum Transport in Semiconductor Nanostructures

Beenakker, C. W. J.; Houten, H. van

doi:10.1016/s0081-1947(08)60091-0

Cited by 1,114 publications

(770 citation statements)

References 479 publications

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“…One lead is assumed to support N 1 ingoing channels and the second one N 2 outgoing channels. In contrast to the random-matrix treatment of [5,7] and work on quantum graphs in [8], our results cover all orders in the inverse number of channels, N = N 1 + N 2 , and thus apply to the experimentally relevant case of few channels [9]. Previously unknown and surprisingly simple expressions for the shot noise arise, both with and without time reversal invariance (see Eq.…”

mentioning

confidence: 82%

Semiclassical prediction for shot noise in chaotic cavities

Braun¹,

Heusler²,

Müller³

et al. 2006

J. Phys. A: Math. Gen.

126

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We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a semiclassical approach we evaluate the contributions of quadruplets of classical trajectories to shot noise. Our approach can be extended to a variety of transport phenomena as illustrated for the crossover between symmetry classes in the presence of a weak magnetic field.PACS numbers: 72.20.My, 72.15.Rn, 05.45.Mt, 03.65.Sq Ballistic chaotic cavities have universal transport properties, just as do disordered conductors. The explanation of such universality cannot rely on any disorder average but must make do with chaos in an individual clean cavity. We shall present here the semiclassical explanation of shot noise, relating the quantum properties of chaotic cavities to the interference between contributions of mutually close classical trajectories. Similar methods have recently been used for explaining universal spectral fluctuations of chaotic quantum systems [1,2], and to calculate the universal mean conductance in [3,4].Following Landauer and Büttiker [6,7], we treat transport as scattering between two leads attached to the cavity. One lead is assumed to support N 1 ingoing channels and the second one N 2 outgoing channels. In contrast to the random-matrix treatment of [5,7] and work on quantum graphs in [8], our results cover all orders in the inverse number of channels, N = N 1 + N 2 , and thus apply to the experimentally relevant case of few channels [9]. Previously unknown and surprisingly simple expressions for the shot noise arise, both with and without time reversal invariance (see Eq. (11) below).The transition amplitudes between ingoing channels a 1 and outgoing channels a 2 define an N 1 × N 2 matrix t = {t a1a2 }. That matrix determines the power of shot noise as P = tr(tt † − tt † tt † ) , in units 2e 3 |V | πh depending on the voltage V ; for us, . . . denotes an average over a small energy interval. Previous work had involved averages over ensembles of matrices t and obtained [5,7] (1) here β = 1 refers to the so-called "orthogonal case" of time-reversal invariant dynamics; if a magnetic field is applied to break time-reversal invariance ("unitary case", β = 2), the second ("weak localization") term disappears. Higher orders in 1 N are as yet unknown. In the semiclassical limit, each transition amplitude t a1a2 is given by a sum over trajectories α leading from an ingoing channel a 1 to an outgoing channel a 2 , t a1a2 ∼ α(a1→a2) Aα √ TH e iSα/h [10]. It can be shown that the absolute value of the initial angle of the relevant trajectories (i.e. the angle enclosed between the initial piece and the direction of the lead) is dictated by the ingoing channel, whereas the final angle is determined by the outgoing channel. The contribution of each trajectory depends on the Heisenberg time T H = Ω (2πh) f −1 , with Ω the volume of the energy shell and f the number of free...

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mentioning

confidence: 82%

Semiclassical prediction for shot noise in chaotic cavities

Braun¹,

Heusler²,

Müller³

et al. 2006

J. Phys. A: Math. Gen.

126

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“…Büttikcr h äs dcvcloped the formalism [12] to trcat anomalies in the integer QIIE due to the absence of local equilibrium, when mcasured with non-ideal contacts. To illustrate this formalism we consider, following [17], a Situation in which the edge channcls at the lower edge are in cquilibrium at chemical potcntial Ep·, while the edge channels at the uppcr edge are not in local equilibrium. The currcnt at the upper edge is then not equipartitioned among the A f edge channels.…”

Section: Integer Edge Channelsmentioning

confidence: 99%

“…We will argue t hat the appearance of both "electron" and "hole" channels in this formula implies a novel limitation to the accuracy of the fractional QHE. Much of the matcrial in the prcsent article is bascd on a review with a wider scope written in collaboration with H. van Ilouten [17].…”

Section: Introductionmentioning

confidence: 99%

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

Beenakker

1991

Quantum Coherence in Mesoscopic Systems

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l IntroductionThe quantum Hall effect (QHE) is the phenomenon that the Hall conductance GH is quantized in units of e 2 /h, äs expressed by the formula G -?T ω (p and q being mutually prime integers). The integer QHE (q = 1) was discovered 10 years ago by von Klitzing, Dorda, and Pepper [1] in the two-dimensional electron gas (2DEG) confined to a Si Inversion layer. The fractional QHE (q > l and odd) was first observed by Tsui, Stornier, and Gossard [2] in the 2DEG at the interface of a Al a; Ga 1 _ ; j.As/GaAs heterostructure. Microscopically the two effects are entirely different. The integer QHE, on the one hand, can be explained satisfactorily in terms of the states of non-interacting electrons in a magnetic field (the Landau levels). The fractional QHE, on the other hand, exists only because of electron-electron interactions [3]. Phenomenologically, however, the integer and fractional QHE are quite similar. In an unbounded 2 DEG this similarity is understood from Laughlin's general argument [4] that: (1) The Hall conductance shows a plateau äs a function of magnetic field (or Fermi energy) whenever the quasi-particle excitations in the bulk of the 2 DEG are localized by disorder; and that: (2) The value of GH on the plateau is precisely an integer multiple p of ee*/h, where e* = e/q is the quasi-particle charge. (The product ee* appears because one e is needed to change the unit of conductance from Amperes per electron Volts to Amperes per Volts). Theory and experiment on the QHE in an unbounded 2 DEG have been reviewed in the books by Prange and Girvin [5] and by Chakraborty and Pietiläinen [6] (see also the article by MacDonald in the present volume).In the past few years, a variety of experiments have uncovered a novel phenomenology of the QHE on short length scales. For example, in small sub-micron-size samples

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“…The measurement of integer numbers of a quantum of conductance (G 0 = 2e 2 /h) is a consequence of the current equipartition in a small number of propagating modes [3]. Very early, this phenomenon was satisfactorily reproduced through two-dimensional (2D) models [4,5].…”

Section: Introductionmentioning

confidence: 99%

Conductance of three-dimensional cross junctions in the quantum ballistic regime

Dacal¹,

Silva

2006

Braz. J. Phys.

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The influence of dimensionality on the conductance of semiconductor cross junctions is investigated in the effective mass approximation and quantum ballistic regime. Our calculations exhibit some similar features for both two-and three-dimensional models, namely the conductance peaks before the fundamental eigenenergy of the quantum wire that represents the sidearms and the zero conductance dip. Despite this, we show that, in general, the conductance and the electronic wave function are strongly affected when the third spatial dimension is taken into account. In other words, we prove that two-dimensional models are not suitable for representing this kind of system.

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Quantum Transport in Semiconductor Nanostructures

Cited by 1,114 publications

References 479 publications

Semiclassical prediction for shot noise in chaotic cavities

Semiclassical prediction for shot noise in chaotic cavities

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

Conductance of three-dimensional cross junctions in the quantum ballistic regime

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